if the pair of linear equations 2x + 3y-5=0 and 4x +6y =k have infinite solutions then the value of k is
Answers
EXPLANATION.
Pair of linear equation has infinite many solution.
⇒ 2x + 3y - 5 = 0. - - - - - (1).
⇒ 4x + 6y = k. - - - - - (2).
⇒ 4x + 6y - k = 0. - - - - - (2).
As we know that,
Conditions of infinite many solutions.
⇒ a₁/a₂ = b₁/b₂ = c₁/c₂.
⇒ a₁ = 2, b₁ = 3, c₁ = -5.
⇒ a₂ = 4, b₂ = 6, c₂ = -k.
Put the values in the conditions, we get.
⇒ 2/4 = 3/6 = (-5)/(-k).
Case = 1.
⇒ 2/4 = (-5)/(-k).
⇒ 1/2 = 5/k.
⇒ k = 10.
Case = 2.
⇒ 3/6 = (-5)/(-k).
⇒ 1/2 = 5/k.
⇒ k = 10.
Value of k = 10.
MORE INFORMATION.
(1) = For unique solutions.
a₁/a₂ ≠ b₁/b₂.
(2) = For no solutions.
a₁/a₂ = b₁/b₂ ≠ c₁/c₂.
Given :-
2x + 3y - 5 = 0
4x + 6y = k
To Find :-
Value of k
Solution :-
We know that
a1/a2 = b1/b2 = c1/c2
So, we need to make the RHS equal
RHS of equation 1 = 0
4x + 6y = k
4x + 6y - k = 0
Now we may solve further
2/4 = 3/6 = -5/-k
2/4 = 3/6 = 5/k
1/2 = 1/2 = 5/k
1/2 = 5/k
2 × 5 = 1 × k
10 = k
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